Finite Group Databasebeta

← #14908048

Subgroups — #14908048

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622806C211yesmaximal, characteristic, complemented
3#13079040C211yesmaximal, characteristic, complemented
4C2×#10622485C211yesmaximal, characteristic, complemented
5#13070674C212yesmaximal, complemented
6#13070670C212yesmaximal, complemented
7#13070660C212yesmaximal, complemented
8#13070650C212yesmaximal, complemented
9#13070371C211yesmaximal, characteristic, complemented
10#13070326C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623363—21no—
14C2×#67003—21no—
15C2×#66957C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C2×#66946—21no—
18C2×C11×M32C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20#10622806—24no—
21#10622804C2211yescharacteristic, complemented
22#10622794C2211yescharacteristic, complemented
23C2×#66892C2212yes—
24#10622788—21no—
25#10622781—21no—
26#10622768C2211yescharacteristic, complemented
27#10622764C2211yescharacteristic, complemented
28C2×#66890C2212yes—
29C2×C8×Dic11C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31C2×#66873—21no—
32#10622521—24no—
33C2×#66864C2212yes—
34C2×D176C2212yes—
35#10622485—21no—
36#10622485—21no—
37#10622485C2212yes—
38#10622485C2212yes—
39C11×#358C2212yescomplemented
40C11×#357C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42Dic11⋊C16C2212yescomplemented
43#10622130C2212yescomplemented
44#10622129C2212yescomplemented
45C2×C11×#41—21no—
46C2×#4339—21no—
47C22×D44—21no—
48C22×C4×D11—41no—
49C11×#135—22no—
50C11×#135—22no—
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×D8C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C2×C11×C4⋊C4—21no—
56#67003—44no—
57#67000—21no—
58#66997—21no—
59C2×#4326—21no—
60C2×#4325—21no—
61#66993—21no—
62#66992—41no—
63#66992—41no—
64#66989—21no—
65C2×#4324—21no—
66C2×#4323—21no—
67C4×C22⋊D11—41no—
68C4×C22⋊D11—41no—
69C2×(C2×D11)⋊C4—41no—
70C2×C4×Dic11D411yescharacteristic
71C22×C11⋊C8D411yescharacteristic
72C2×Dic44C2311yescharacteristic
73#66957—22no—
74#66957—22no—
75C2×D88—21no—
76C2×D88—22no—
77C2×D88D414yescomplemented
78C2×D88C2311yescharacteristic
79C2×D88C2312yes—
80C2×#4314—21no—
81#66946—22no—
82#66946—22no—
83#66946—41no—
84#66946—41no—
85C11×M32—22no—
86C2×C11×C16C2312yes—
87C11×#107—21no—
88C11×#107C2312yes—
89#66892—24no—
90#66890—24no—
91C8×Dic11D411yescharacteristic
92C8×Dic11D411yescharacteristic
93C8×Dic11C2311yescharacteristic
94C8×Dic11C2311yescharacteristic
95#66876—22no—
96C2×C11⋊C16C2312yes—
97#66873—22no—
98#66873—22no—
99#66864—24no—
100D176—24no—
101#33580—111nomaximal, Sylow
102C23×D11—41no—
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114C22×Dic11D811yescharacteristic
115C22×Dic11D811yescharacteristic
116#4339—42no—
117#4339—42no—
118C2×D44—24no—
119C2×D44—22no—
120C2×D44—21no—
121C2×D44—41no—
122C2×D44—42no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—41no—
126C2×C4×D11—84no—
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×SD16—42no—
131C11×D8—21no—
132C11×D8—21no—
133C2×C8×C11C2×D412yes—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11#4112yes—
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—22no—
138C11×C4⋊C4—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141#4326—42no—
142#4325—42no—
143#4324—42no—
144#4323—42no—
145(C2×D11)⋊C4—42no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151C4×Dic11D811yescharacteristic
152C4×Dic11D811yescharacteristic
153C4×Dic11C2×D411yescharacteristic
154C4×Dic11C2×D411yescharacteristic
155C2×C11⋊C8—22no—
156C2×C11⋊C8C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158Dic44—21no—
159Dic44—21no—
160D88—24no—
161D88—21no—
162D88—22no—
163D88—21no—
164D88C2×D414yes—
165#4314—42no—
166C11×C16—22no—
167C11⋊C16—22no—
168C2×#509—111no—
169C2×#509—111no—
170#3147—111no—
171C2×C4×D8—111no—
172#2210—112no—
173#2210—112no—
174#2208—112no—
175#2206—112no—
176#2150—111no—
177#2139—111no—
178#2139D1111yescharacteristic, complemented
179C23×C11—41no—
180C23×C11C2×D811yescharacteristic
181C22×D11—42no—
182C22×D11—44no—
183C22×D11—41no—
184C22×D11—82no—
185C22×D11—82no—
186Q8×C11—41no—
187Q8×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—82no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—82no—
194C2×C4×C11—82no—
195C2×C4×C11#12112yes—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—82no—
200C22⋊D11—82no—
201C22⋊D11—82no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11C2×D811yescharacteristic
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209D44—24no—
210D44—41no—
211D44—42no—
212D44—41no—
213D44—44no—
214C4×D11—84no—
215C4×D11—82no—
216C4×D11—84no—
217Dic22—41no—
218Dic22—41no—
219C8×C11#12112yes—
220C8×C11C22×D411yescharacteristic
221C8×C11C2×#4111yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224C2×#135—111no—
225C2×#135—221no—
226C2×#135C2×D1111yescharacteristic
227C22×D8—111no—
228#532—221no—
229C2×C4×D4—221no—
230#509—224no—
231#509—224no—
232C2×SD32—112no—
233C2×SD32—112no—
234C2×D16—112no—
235C2×D16—112no—
236C2×M32—111no—
237C2×M32C2×D1111yescharacteristic
238#495—111no—
239#495—111no—
240#495—221no—
241#494—111no—
242#493—111no—
243#492—221no—
244C4×D8—112no—
245C4×D8—112no—
246C4×D8—221no—
247C4×D8—221no—
248C2×#107C2×D1111yescharacteristic
249C2×#102—221no—
250C2×C4×C8—111no—
251C4⋊C16—112no—
252C4⋊C16—112no—
253#358—112no—
254#358C2×D1112yescomplemented
255#357—112no—
256#357C2×D1112yescomplemented
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11#45912yes—
263C22×C11C22×D811yescharacteristic
264C2×D11—44no—
265C2×D11—88no—
266C2×D11—82no—
267C2×D11—82no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—82no—
272C4×C11—81no—
273C4×C11#45912yes—
274C4×C11C2×#12111yescharacteristic
275C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
276Dic11—21no—
277Dic11—21no—
278Dic11—21no—
279Dic11—81no—
280Dic11#50912yescomplemented
281C2×#41—21no—
282C2×#41—221no—
283C22×D4—221no—
284C23×C4—441no—
285#135—22no—
286#135—22no—
287#135—222no—
288#135—222no—
289#135—444no—
290C2×Q16—111no—
291C2×Q16—221no—
292C2×Q16C22×D1111yescharacteristic
293C2×SD16—21no—
294C2×SD16—221no—
295C2×SD16—221no—
296C2×SD16—221no—
297C2×D8—114no—
298C2×D8—112no—
299C2×D8—111no—
300C2×D8—221no—
301C2×D8—222no—
302C2×D8—221no—
303C2×D8C22×D1111yescharacteristic
304C22×C8—111no—
305C22×C8C22×D1111yescharacteristic
306C4⋊Q8—221no—
307#127—221no—
308#124—221no—
309#124—221no—
310#121—441no—
311#121—441no—
312C4×D4—222no—
313C4×D4—222no—
314C4×D4—441no—
315C4×D4—441no—
316C4×D4—441no—
317C4×D4—441no—
318C2×C4⋊C4—21no—
319C2×C22⋊C4—441no—
320C2×C42—111no—
321SD32—224no—
322SD32—224no—
323D16—224no—
324D16—224no—
325M32—22no—
326M32—222no—
327C2×C16—112no—
328C2×C16C22×D1112yes—
329#107—21no—
330#107C22×D1112yes—
331#102—222no—
332#102—222no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8—111no—
336C4×C8—111no—
337C2×C11—22no—
338C2×C11—161no—
339C2×C11C2×#45911yescharacteristic
340C2×C11C2×#50911yescharacteristic
341C2×C11#341411yescharacteristic
342D11—84no—
343D11—161no—
344C24—441no—
345#41—42no—
346#41—42no—
347#41—442no—
348#41—442no—
349C2×Q8—21no—
350C2×Q8—221no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—224no—
354C2×D4—222no—
355C2×D4—221no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—442no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—442no—
366C22×C4—442no—
367C22×C4—441no—
368C22×C4—884no—
369C22×C4D4×D1111yescharacteristic
370Q16—21no—
371Q16—21no—
372Q16—221no—
373Q16—221no—
374Q16—442no—
375SD16—42no—
376SD16—442no—
377SD16—442no—
378SD16—442no—
379D8—21no—
380D8—21no—
381D8—114no—
382D8—224no—
383D8—222no—
384D8—221no—
385D8—221no—
386D8—442no—
387C2×C8—111no—
388C2×C8—111no—
389C2×C8—222no—
390C2×C8#433912yes—
391C2×C8D4×D1111yescharacteristic
392C2×C8D4×D1112yes—
393C2×C8C23×D1111yescharacteristic
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C22⋊C4—442no—
399C22⋊C4—442no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C42—111no—
405C42—111no—
406C42—111no—
407C42—111no—
408C16—22no—
409C16—222no—
410C11#3358011yescharacteristic, complemented, Sylow
411C23—41no—
412C23—442no—
413C23—444no—
414C23—441no—
415C23—882no—
416C23—882no—
417C23D8×D1111yescharacteristic
418Q8—41no—
419Q8—41no—
420Q8—441no—
421Q8—441no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—224no—
426D4—441no—
427D4—442no—
428D4—441no—
429D4—444no—
430D4—882no—
431D4—882no—
432D4—882no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—111no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—111no—
441C2×C4—222no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—884no—
445C2×C4—884no—
446C2×C4—882no—
447C2×C4#6693712yes—
448C2×C4D8×D1111yescharacteristic
449C2×C4#6696712yes—
450C2×C4C2×D4×D1111yescharacteristic
451C8—221no—
452C8—221no—
453C8#6693712yes—
454C8C2×#433911yescharacteristic
455C8C2×D4×D1111yescharacteristic
456C22—21no—
457C22—21no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—444no—
462C22—888no—
463C22—882no—
464C22—882no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22#1062239912yes—
469C22C2×D8×D1111yescharacteristic
470C4—81no—
471C4—82no—
472C4—112no—
473C4—221no—
474C4—221no—
475C4—221no—
476C4—881no—
477C4#1062239912yes—
478C4C2×#6693711yescharacteristic
479C4C2×#6696711yescharacteristic
480C2—22no—
481C2—161no—
482C2—884no—
483C2—1761no—
484C2C2×#1062239911yescharacteristic
485C2D11×#50911yescharacteristic
486C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
hypercenter#2139D11
hypocenterC11#33580
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622806C2semidirect
3. #13079040C2semidirect
4. C2×#10622485C2semidirect
5. #13070674C2semidirect
6. #13070670C2semidirect
7. #13070660C2semidirect
8. #13070650C2semidirect
9. #13070371C2semidirect
10. #13070326C2semidirect
11. C11×#2139C2semidirect
21. #10622804C22semidirect
22. #10622794C22semidirect
26. #10622768C22semidirect
27. #10622764C22semidirect
39. C11×#358C22semidirect
40. C11×#357C22semidirect
41. Dic11⋊C16C22semidirect
42. Dic11⋊C16C22semidirect
43. #10622130C22semidirect
44. #10622129C22semidirect
77. C2×D88D4semidirect
178. #2139D11semidirect
254. #358C2×D11semidirect
256. #357C2×D11semidirect
280. Dic11#509semidirect
410. C11#33580semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225212
C2×#106228062
#130790402
C2×#106224852
#130706742
#130706702
#130706602
#130706502
#130703712
#130703262
C11×#21392
#3358011